953 research outputs found
Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models
We investigate the influence of aperiodic modulations of the exchange
interactions between nearest-neighbour rows on the phase transition of the
two-dimensional eight-state Potts model. The systems are studied numerically
through intensive Monte Carlo simulations using the Swendsen-Wang cluster
algorithm for different aperiodic sequences. The transition point is located
through duality relations, and the critical behaviour is investigated using FSS
techniques at criticality. While the pure system exhibits a first-order
transition, we show that the deterministic fluctuations resulting from the
aperiodic coupling distribution are liable to modify drastically the physical
properties in the neighbourhood of the transition point. For strong enough
fluctuations of the sequence under consideration, a second-order phase
transition is induced. The exponents , and
are obtained at the new fixed point and crossover effects are
discussed. Surface properties are also studied.Comment: LaTeX file with EPJB macro package, 11 pages, 16 postscript figures,
to appear in Eur. Phys. J.
The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions
We present an analytic approach to study concurrent influence of quenched
non-magnetic site-dilution and finiteness of the lattice on the 2D XY model.
Two significant deeply connected features of this spin model are: a special
type of ordering (quasi-long-range order) below a certain temperature and a
size-dependent mean value of magnetisation in the low-temperature phase that
goes to zero (according to the Mermin-Wagner-Hohenberg theorem) in the
thermodynamic limit. We focus our attention on the asymptotic behaviour of the
spin-spin correlation function and the probability distribution of
magnetisation. The analytic approach is based on the spin-wave approximation
valid for the low-temperature regime and an expansion in the parameters which
characterise the deviation from completely homogeneous configuration of
impurities. We further support the analytic considerations by Monte Carlo
simulations performed for different concentrations of impurities and compare
analytic and MC results. We present as the main quantitative result of the work
the exponent of the spin-spin correlation function power law decay. It is non
universal depending not only on temperature as in the pure model but also on
concentration of magnetic sites. This exponent characterises also the vanishing
of magnetisation with increasing lattice size.Comment: 13 pages, 7 eps figures, style files include
Numerical investigation of logarithmic corrections in two-dimensional spin models
The analysis of correlation function data obtained by Monte Carlo simulations
of the two-dimensional 4-state Potts model, XY model, and self-dual disordered
Ising model at criticality are presented. We study the logarithmic corrections
to the algebraic decay exhibited in these models. A conformal mapping is used
to relate the finite-geometry information to that of the infinite plane.
Extraction of the leading singularity is altered by the expected logarithmic
corrections, and we show numerically that both leading and correction terms are
mutually consistent
Nematic phase transitions in two-dimensional systems
Simulations of nematic-isotropic transition of liquid crystals in two
dimensions are performed using an O(2) vector model characterised by non linear
nearest neighbour spin interaction governed by the fourth Legendre polynomial
. The system is studied through standard Finite-Size Scaling and
conformal rescaling of density profiles or correlation functions. The low
temperature limit is discussed in the spin wave approximation and confirms the
numerical results, while the value of the correlation function exponent at the
deconfining transition seems controversial.Comment: Talk given at Statphys 2005, Lviv, Ukrain
Network harness: bundles of routes in public transport networks
Public transport routes sharing the same grid of streets and tracks are often
found to proceed in parallel along shorter or longer sequences of stations.
Similar phenomena are observed in other networks built with space consuming
links such as cables, vessels, pipes, neurons, etc. In the case of public
transport networks (PTNs) this behavior may be easily worked out on the basis
of sequences of stations serviced by each route. To quantify this behavior we
use the recently introduced notion of network harness. It is described by the
harness distribution P(r,s): the number of sequences of s consecutive stations
that are serviced by r parallel routes. For certain PTNs that we have analyzed
we observe that the harness distribution may be described by power laws. These
power laws observed indicate a certain level of organization and planning which
may be driven by the need to minimize the costs of infrastructure and secondly
by the fact that points of interest tend to be clustered in certain locations
of a city. This effect may be seen as a result of the strong interdependence of
the evolutions of both the city and its PTN.
To further investigate the significance of the empirical results we have
studied one- and two-dimensional models of randomly placed routes modeled by
different types of walks. While in one dimension an analytic treatment was
successful, the two dimensional case was studied by simulations showing that
the empirical results for real PTNs deviate significantly from those expected
for randomly placed routes.Comment: 12 pages, 24 figures, paper presented at the Conference ``Statistical
Physics: Modern Trends and Applications'' (23-25 June 2009, Lviv, Ukaine)
dedicated to the 100th anniversary of Mykola Bogolyubov (1909-1992
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